Bell will be remembered
for being the first who realize that, in quantum theory, correlations
between outcomes of jointly measurable observables violate certain
inequalities satisfied by local (and noncontextual) hidden variables
theories. Then, Tsirelson has to be remembered as the first who
realize that violations of Bell inequalities are themselves upper
bounded in nature. Similarly, Popescu and Rohrlich have to be
remembered for being the first ones who asked the "right"
question: Why? What reasons or physical principles enforce the
violation of Bell inequalities up, but not beyond, certain limits? We
will report some recent results related to this question.
Specifically, we will identify which Bell and noncontextuality
inequalities are violated in nature, which violations are possible
and which principle explains that higher violations cannot occur.